(CNN)-- House Speaker John Boehner said Thursday he was confident the House would re-elect him speaker, but conceded a few fellow Republicans would likely vote against him.
Some conservative activists have called on the House to oust Boehner following the passage of a deal to avoid the fiscal cliff. The deal raised tax rates for American households earning more than $450,000 per year. While Boehner made a list-minute effort to include spending cuts in the deal, the measure passed without them.
Rep. Eric Cantor, the House Majority Leader, also expressed confidence Thursday that Boehner would be re-elected speaker, saying "absolutely" when asked whether his colleagues would support Boehner for another term in the top post.
Cantor voted "no" on the final fiscal cliff deal Tuesday night, breaking with Boehner, who cast a "yea" vote. A majority of House Republicans voted against the bill, though earlier Tuesday it passed with a large majority in the Senate.
When CNN asked Cantor if the speaker will be re-elected he replied "absolutely."
The speaker also confirmed that he's told his GOP colleagues that he's going to back off attempting one-on-one negotiations with President Barack Obama to pre-cook major deals, after the two men failed to reach an agreement averting the fiscal cliff.
The deal that eventually passed was brokered by Vice President Joe Biden and Sen. Mitch McConnell, the Republican leader in the Senate.
"Regular order works best," Boehner said – meaning he'll follow normal legislative process in the future by introducing bills in the House that would eventually be sent to the president.
Boehner added that he's "always happy to talk to the president."